Geodesic
On reconstruction of an input for parabolic equation on infinite time interval
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 30-41.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a parabolic equation we consider a problem of dynamic reconstruction of inputs from measurements of phase coordinates on an infinite time interval. The paper presents an algorithm based on constructions of the theory of dynamic inversion. The algorithm is stable with respect to informational noises and computational errors.
Keywords: dynamic inverse problems, reconstruction of disturbances. 
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M. S. Blizorukova; V. I. Maksimov. On reconstruction of an input for parabolic equation on infinite time interval. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 30-41. http://geodesic.mathdoc.fr/item/IVM_2014_8_a2/

[1] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[2] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, M., 1979 | MR

[3] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[4] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, Novosibirsk, 1980 | MR

[5] Kryazhimskii A. V., Osipov Yu. S., “O modelirovanii upravleniya v dinamicheskoi sisteme”, Izv. AN SSSR. Tekhn. kibernetika, 1983, no. 2, 51–60 | MR

[6] Osipov Yu. S., Kryazhimskii A. V., Inverse problems for ordinary differential equations: dynamical solutions, Gordon and Breach, Basel, 1995 | MR | Zbl

[7] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., Metody dinamicheskogo vosstanovleniya vkhodov upravlyaemykh sistem, UrO RAN, Ekaterinburg, 2011

[8] Maksimov V. I., Zadachi dinamicheskogo vosstanovleniya vkhodov beskonechnomernykh sistem, Ekaterinburg, 2000

[9] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, M., 1974 | MR

[10] Osipov Yu. S., Kryazhimskii A. V., Maksimov V. I., “Metod ekstremalnogo sdviga N. N. Krasovskogo i zadachi granichnogo upravleniya”, Avtomatika i telemekhanika, 2009, no. 4, 18–30 | MR | Zbl

[11] Maksimov V. I., “Ob odnom algoritme vosstanovleniya intensivnosti funktsii istochnika”, Tr. MIRAN im. V. A. Steklova, 277, 2012, 178–191 | MR

[12] Maksimov V. I., “On reconstruction of boundary controls in a parabolic equation”, Advances in Diff. Equat., 14:11–12 (2009), 1193–1211 | MR | Zbl

[13] Kryazhimskii A. V., Maksimov V. I., “On rough inversion of a dynamical system with a disturbance”, J. Inv. Ill-Posed Problems, 16 (2008), 1–14 | DOI | MR

[14] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

[15] Barbu V., Optimal control of variational inequalities, Pitman Advanced Publishing Program, London, 1984 | MR | Zbl